Question

In the given figure, PO and RS are two mirrors placed parallel to each other. An incident ray
AB strikes the mirror P9 at B, the reflected ray moves along the path BC and strikes the
mirror RS at C and again reflects back along CD. Prove that AB Il CD​

Answer 1

join AD.

then AD is parallel to PQ.

name the point H on the line which cuts BC.

Now, then triangle ABH is equal to triangle DCH

because PQ is parrallel to BC and AD is parallel to both.

we also know that area of triangle ABH is equal to area of triangle DCH because they on same base(AD) and between same parallel lines.

thereforein triangle ABH and DCH

AB=CD and AB is also parallel to CD.

HENCE , PROVED

Answer 2

Answer:

Step-by-step explanation:

PQ || RS ⇒ BL || CM

[∵ BL || PQ and CM || RS]

Now, BL || CM and BC is a transversal.

∴ ∠LBC = ∠MCB …(1) [Alternate interior angles]

Since, angle of incidence = Angle of reflection

∠ABL = ∠LBC and ∠MCB = ∠MCD

⇒ ∠ABL = ∠MCD …(2) [By (1)]

Adding (1) and (2), we get

∠LBC + ∠ABL = ∠MCB + ∠MCD

⇒ ∠ABC = ∠BCD

i. e., a pair of alternate interior angles are equal.

∴ AB || CD.